TSTP Solution File: NUN073+2 by Princess---230619

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Princess---230619
% Problem  : NUN073+2 : TPTP v8.1.2. Released v7.3.0.
% Transfm  : none
% Format   : tptp
% Command  : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s

% Computer : n025.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Thu Aug 31 12:51:02 EDT 2023

% Result   : Theorem 5.47s 1.47s
% Output   : Proof 6.95s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : NUN073+2 : TPTP v8.1.2. Released v7.3.0.
% 0.00/0.13  % Command  : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.34  % Computer : n025.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit : 300
% 0.13/0.34  % WCLimit  : 300
% 0.13/0.34  % DateTime : Sun Aug 27 09:40:39 EDT 2023
% 0.13/0.35  % CPUTime  : 
% 0.20/0.61  ________       _____
% 0.20/0.61  ___  __ \_________(_)________________________________
% 0.20/0.61  __  /_/ /_  ___/_  /__  __ \  ___/  _ \_  ___/_  ___/
% 0.20/0.61  _  ____/_  /   _  / _  / / / /__ /  __/(__  )_(__  )
% 0.20/0.61  /_/     /_/    /_/  /_/ /_/\___/ \___//____/ /____/
% 0.20/0.61  
% 0.20/0.61  A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.20/0.61  (2023-06-19)
% 0.20/0.61  
% 0.20/0.61  (c) Philipp Rümmer, 2009-2023
% 0.20/0.61  Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.20/0.61                Amanda Stjerna.
% 0.20/0.61  Free software under BSD-3-Clause.
% 0.20/0.61  
% 0.20/0.61  For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.20/0.61  
% 0.20/0.62  Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.20/0.63  Running up to 7 provers in parallel.
% 0.20/0.64  Prover 0: Options:  +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.20/0.64  Prover 1: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.20/0.64  Prover 2: Options:  +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.20/0.64  Prover 3: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.20/0.64  Prover 4: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.20/0.64  Prover 6: Options:  -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 0.20/0.64  Prover 5: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 2.63/1.05  Prover 4: Preprocessing ...
% 2.63/1.05  Prover 1: Preprocessing ...
% 2.63/1.09  Prover 6: Preprocessing ...
% 2.63/1.09  Prover 2: Preprocessing ...
% 2.63/1.09  Prover 0: Preprocessing ...
% 2.63/1.09  Prover 3: Preprocessing ...
% 2.63/1.09  Prover 5: Preprocessing ...
% 4.56/1.31  Prover 1: Warning: ignoring some quantifiers
% 4.56/1.33  Prover 4: Warning: ignoring some quantifiers
% 4.56/1.33  Prover 1: Constructing countermodel ...
% 4.56/1.33  Prover 6: Proving ...
% 4.56/1.33  Prover 5: Proving ...
% 4.56/1.33  Prover 2: Proving ...
% 4.56/1.35  Prover 3: Warning: ignoring some quantifiers
% 4.56/1.35  Prover 4: Constructing countermodel ...
% 4.56/1.36  Prover 3: Constructing countermodel ...
% 4.56/1.36  Prover 0: Proving ...
% 5.47/1.47  Prover 0: proved (838ms)
% 5.47/1.47  
% 5.47/1.47  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 5.47/1.47  
% 5.47/1.48  Prover 2: proved (839ms)
% 5.47/1.48  
% 5.47/1.48  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 5.47/1.48  
% 5.47/1.48  Prover 6: stopped
% 5.47/1.48  Prover 5: stopped
% 5.47/1.48  Prover 4: Found proof (size 13)
% 5.47/1.48  Prover 3: stopped
% 5.47/1.48  Prover 4: proved (837ms)
% 5.47/1.49  Prover 7: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 5.47/1.49  Prover 8: Options:  +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 5.47/1.49  Prover 10: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 5.47/1.49  Prover 13: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 5.47/1.49  Prover 11: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 5.47/1.50  Prover 1: stopped
% 6.07/1.53  Prover 10: Preprocessing ...
% 6.07/1.53  Prover 11: Preprocessing ...
% 6.07/1.54  Prover 7: Preprocessing ...
% 6.07/1.54  Prover 13: Preprocessing ...
% 6.07/1.55  Prover 8: Preprocessing ...
% 6.07/1.55  Prover 10: stopped
% 6.07/1.55  Prover 7: stopped
% 6.07/1.56  Prover 13: stopped
% 6.07/1.56  Prover 11: stopped
% 6.51/1.61  Prover 8: Warning: ignoring some quantifiers
% 6.51/1.62  Prover 8: Constructing countermodel ...
% 6.51/1.62  Prover 8: stopped
% 6.51/1.62  
% 6.51/1.63  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 6.51/1.63  
% 6.51/1.63  % SZS output start Proof for theBenchmark
% 6.51/1.63  Assumptions after simplification:
% 6.51/1.63  ---------------------------------
% 6.51/1.63  
% 6.51/1.63    (axiom_1)
% 6.51/1.66     ? [v0: $i] : ($i(v0) &  ! [v1: $i] : (v1 = v0 |  ~ (r1(v1) = 0) |  ~ $i(v1))
% 6.51/1.66      &  ! [v1: int] : (v1 = 0 |  ~ (r1(v0) = v1)))
% 6.51/1.66  
% 6.51/1.66    (axiom_3a)
% 6.51/1.66     ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] : (v1 = v0 |  ~ (r2(v1, v2) = 0) |  ~
% 6.51/1.66      (r2(v0, v2) = 0) |  ~ $i(v2) |  ~ $i(v1) |  ~ $i(v0))
% 6.51/1.66  
% 6.51/1.66    (axiom_7a)
% 6.51/1.66     ! [v0: $i] :  ! [v1: $i] : ( ~ (r2(v0, v1) = 0) |  ~ (r1(v1) = 0) |  ~ $i(v1)
% 6.51/1.66      |  ~ $i(v0))
% 6.51/1.66  
% 6.51/1.66    (oneuneqtwo)
% 6.51/1.66     ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] :  ? [v3: $i] : (r2(v3, v0) = 0 &
% 6.51/1.66      r2(v2, v1) = 0 & r2(v1, v0) = 0 & r1(v3) = 0 & r1(v2) = 0 & $i(v3) & $i(v2)
% 6.51/1.66      & $i(v1) & $i(v0))
% 6.51/1.66  
% 6.51/1.66  Further assumptions not needed in the proof:
% 6.51/1.66  --------------------------------------------
% 6.51/1.66  axiom_1a, axiom_2, axiom_2a, axiom_3, axiom_4, axiom_4a, axiom_5a, axiom_6a
% 6.51/1.66  
% 6.51/1.66  Those formulas are unsatisfiable:
% 6.51/1.66  ---------------------------------
% 6.51/1.66  
% 6.51/1.66  Begin of proof
% 6.90/1.66  | 
% 6.90/1.67  | DELTA: instantiating (axiom_1) with fresh symbol all_6_0 gives:
% 6.90/1.67  |   (1)  $i(all_6_0) &  ! [v0: any] : (v0 = all_6_0 |  ~ (r1(v0) = 0) |  ~
% 6.90/1.67  |          $i(v0)) &  ! [v0: int] : (v0 = 0 |  ~ (r1(all_6_0) = v0))
% 6.90/1.67  | 
% 6.90/1.67  | ALPHA: (1) implies:
% 6.90/1.67  |   (2)   ! [v0: any] : (v0 = all_6_0 |  ~ (r1(v0) = 0) |  ~ $i(v0))
% 6.90/1.67  | 
% 6.90/1.67  | DELTA: instantiating (oneuneqtwo) with fresh symbols all_13_0, all_13_1,
% 6.90/1.67  |        all_13_2, all_13_3 gives:
% 6.90/1.67  |   (3)  r2(all_13_0, all_13_3) = 0 & r2(all_13_1, all_13_2) = 0 & r2(all_13_2,
% 6.90/1.67  |          all_13_3) = 0 & r1(all_13_0) = 0 & r1(all_13_1) = 0 & $i(all_13_0) &
% 6.90/1.67  |        $i(all_13_1) & $i(all_13_2) & $i(all_13_3)
% 6.90/1.67  | 
% 6.90/1.67  | ALPHA: (3) implies:
% 6.90/1.67  |   (4)  $i(all_13_3)
% 6.90/1.67  |   (5)  $i(all_13_2)
% 6.90/1.67  |   (6)  $i(all_13_1)
% 6.90/1.67  |   (7)  $i(all_13_0)
% 6.90/1.67  |   (8)  r1(all_13_1) = 0
% 6.90/1.67  |   (9)  r1(all_13_0) = 0
% 6.90/1.67  |   (10)  r2(all_13_2, all_13_3) = 0
% 6.90/1.67  |   (11)  r2(all_13_1, all_13_2) = 0
% 6.90/1.67  |   (12)  r2(all_13_0, all_13_3) = 0
% 6.90/1.67  | 
% 6.95/1.68  | GROUND_INST: instantiating (2) with all_13_1, simplifying with (6), (8) gives:
% 6.95/1.68  |   (13)  all_13_1 = all_6_0
% 6.95/1.68  | 
% 6.95/1.68  | GROUND_INST: instantiating (2) with all_13_0, simplifying with (7), (9) gives:
% 6.95/1.68  |   (14)  all_13_0 = all_6_0
% 6.95/1.68  | 
% 6.95/1.68  | GROUND_INST: instantiating (axiom_3a) with all_13_2, all_13_0, all_13_3,
% 6.95/1.68  |              simplifying with (4), (5), (7), (10), (12) gives:
% 6.95/1.68  |   (15)  all_13_0 = all_13_2
% 6.95/1.68  | 
% 6.95/1.68  | COMBINE_EQS: (14), (15) imply:
% 6.95/1.68  |   (16)  all_13_2 = all_6_0
% 6.95/1.68  | 
% 6.95/1.68  | REDUCE: (11), (13), (16) imply:
% 6.95/1.68  |   (17)  r2(all_6_0, all_6_0) = 0
% 6.95/1.68  | 
% 6.95/1.68  | REDUCE: (8), (13) imply:
% 6.95/1.68  |   (18)  r1(all_6_0) = 0
% 6.95/1.68  | 
% 6.95/1.68  | REDUCE: (5), (16) imply:
% 6.95/1.68  |   (19)  $i(all_6_0)
% 6.95/1.68  | 
% 6.95/1.68  | GROUND_INST: instantiating (axiom_7a) with all_6_0, all_6_0, simplifying with
% 6.95/1.68  |              (17), (18), (19) gives:
% 6.95/1.68  |   (20)  $false
% 6.95/1.68  | 
% 6.95/1.68  | CLOSE: (20) is inconsistent.
% 6.95/1.68  | 
% 6.95/1.68  End of proof
% 6.95/1.68  % SZS output end Proof for theBenchmark
% 6.95/1.68  
% 6.95/1.68  1067ms
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